Finite Group Databasebeta

← #404139

Subgroups — #404139

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2346C211yesmaximal, characteristic
2C2×#2059C211yesmaximal, characteristic, complemented
3C2×#1989C211yesmaximal, characteristic, complemented
4#15216C211yesmaximal, characteristic
5#11293C211yesmaximal, characteristic, complemented
6#11292C211yesmaximal, characteristic, complemented
7#11227C211yesmaximal, characteristic, complemented
8#11096C211yesmaximal, characteristic
9#11095C211yesmaximal, characteristic
10#11042C211yesmaximal, characteristic
11#10908C211yesmaximal, characteristic, complemented
12#10907C211yesmaximal, characteristic, complemented
13#10807C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic
15#10731C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23#2346—24no—
24#2346—24no—
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#388—21no—
28C2×#388—21no—
29C2×#382—21no—
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×#376—21no—
37#2059—24no—
38#1989—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1442—21no—
57#1442—21no—
58#1439—21no—
59#1439—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C24×C4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×#125—22no—
69C2×#125—22no—
70C2×#125—22no—
71C2×#125—22no—
72C2×#125—41no—
73C2×#125—41no—
74C2×#117—22no—
75C2×#117—22no—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117Q814yes—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4D411yescharacteristic
97C22×C22⋊C4D411yescharacteristic
98C22×C42—21no—
99C22×C42—21no—
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C2×#107—22no—
104C2×#107—22no—
105C2×#107—41no—
106C2×#106—22no—
107C2×#106—22no—
108C2×#106—41no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—41no—
111C2×C4⋊C8—41no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—41no—
117C2×C22⋊C8—41no—
118#389—22no—
119#389—22no—
120#389—22no—
121#389D414yes—
122#388—28no—
123#388—28no—
124#382—28no—
125#380—22no—
126#380—22no—
127#380—22no—
128#380—22no—
129#380—41no—
130#380—41no—
131C4×C4⋊C4—22no—
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4D414yes—
135C4×C22⋊C4—22no—
136C4×C22⋊C4—22no—
137#376—28no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95D411yescharacteristic
152C2×#95D411yescharacteristic
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#336—22no—
168#336—22no—
169#336—22no—
170C25C2×D411yescharacteristic
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×Q812yes—
197C23×C4#4112yes—
198C23×C4C2411yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8#4112yes—
226C22×C8#4112yes—
227#125—28no—
228#125—44no—
229#125—44no—
230#125—44no—
231#117—28no—
232#117—28no—
233#117—28no—
234#117—28no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—81no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4C2×D412yes—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×D412yes—
288C2×C4⋊C4C2×D412yes—
289C2×C4⋊C4C2×Q812yes—
290C2×C4⋊C4C2×Q812yes—
291C2×C4⋊C4#4112yes—
292C2×C4⋊C4#4112yes—
293C2×C4⋊C4#4112yes—
294C2×C4⋊C4#4112yes—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—81no—
310C2×C22⋊C4—81no—
311C2×C22⋊C4—81no—
312C2×C22⋊C4—81no—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—24no—
321C2×C42—24no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42C2×D412yes—
333C2×C42C2×D412yes—
334#107—44no—
335#106—44no—
336C4⋊C8—44no—
337C22⋊C8—44no—
338C22⋊C8—44no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—22no—
345#95—22no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—81no—
351#95—81no—
352#95—81no—
353#95—81no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24C22⋊Q812yes—
369C24C22×D411yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4#12012yes—
486C22×C4#12012yes—
487C22×C4C22⋊Q812yes—
488C22×C4#13512yes—
489C22×C4C22×D411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C22×Q811yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C42−1+411yescharacteristic
502C22×C42−1+411yescharacteristic
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—84no—
564C4⋊C4—84no—
565C4⋊C4C22⋊Q814yes—
566C4⋊C4C22⋊Q814yes—
567C22⋊C4—216no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—84no—
571C22⋊C4—84no—
572C22⋊C4—84no—
573C42—216no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—48no—
579C42—48no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23C2×#12011yescharacteristic
620C23C2×C22⋊Q811yescharacteristic
621C23#52511yescharacteristic
622C23#54611yescharacteristic
623C23#54611yescharacteristic
624C23#54711yescharacteristic
625C23#54711yescharacteristic
626C23C2×#13511yescharacteristic
627C23#57511yescharacteristic
628C23#57511yescharacteristic
629C23#57511yescharacteristic
630C23#57611yescharacteristic
631C23#57711yescharacteristic
632C23#57711yescharacteristic
633C23#57811yescharacteristic
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4C2×C22⋊Q811yescharacteristic
734C2×C4C2×C22⋊Q811yescharacteristic
735C2×C4#52511yescharacteristic
736C2×C4#52511yescharacteristic
737C2×C4#52511yescharacteristic
738C2×C4#52911yescharacteristic
739C2×C4#52911yescharacteristic
740C2×C4#53211yescharacteristic
741C2×C4#53311yescharacteristic
742C2×C4#53311yescharacteristic
743C2×C4#53511yescharacteristic
744C2×C4#53611yescharacteristic
745C2×C4#54211yescharacteristic
746C2×C4#54211yescharacteristic
747C2×C4#54411yescharacteristic
748C2×C4#54411yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#54811yescharacteristic
752C2×C4#54811yescharacteristic
753C2×C4#55111yescharacteristic
754C2×C4#55111yescharacteristic
755C2×C4#55211yescharacteristic
756C2×C4#55211yescharacteristic
757C2×C4#55511yescharacteristic
758C2×C4#55511yescharacteristic
759C2×C4#55611yescharacteristic
760C2×C4#55611yescharacteristic
761C8—42no—
762C8—42no—
763C8—81no—
764C8—81no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22#240411yescharacteristic
781C22#243211yescharacteristic
782C22#243811yescharacteristic
783C22#243811yescharacteristic
784C22#247411yescharacteristic
785C22#247411yescharacteristic
786C22#284811yescharacteristic
787C22#300211yescharacteristic
788C22#300511yescharacteristic
789C22#301211yescharacteristic
790C22#301311yescharacteristic
791C22#307611yescharacteristic
792C22#308011yescharacteristic
793C22#308311yescharacteristic
794C22#308411yescharacteristic
795C22#310211yescharacteristic
796C22#311111yescharacteristic
797C22#311911yescharacteristic
798C22#312011yescharacteristic
799C22#330311yescharacteristic
800C22#330511yescharacteristic
801C22#331511yescharacteristic
802C22#331711yescharacteristic
803C22#331911yescharacteristic
804C22#332111yescharacteristic
805C22#332311yescharacteristic
806C22#332711yescharacteristic
807C22#333611yescharacteristic
808C22#333711yescharacteristic
809C22#334711yescharacteristic
810C22#334711yescharacteristic
811C22#334811yescharacteristic
812C22#334811yescharacteristic
813C22#335111yescharacteristic
814C22#335211yescharacteristic
815C4—42no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—44no—
820C4—44no—
821C4—81no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—161no—
827C4—161no—
828C4#239611yescharacteristic
829C4#243911yescharacteristic
830C4#243911yescharacteristic
831C4#247711yescharacteristic
832C4#247711yescharacteristic
833C4#259911yescharacteristic
834C4#261011yescharacteristic
835C4#262811yescharacteristic
836C2—82no—
837C2#1488711yescharacteristic
838C2#2396511yescharacteristic
839C2#2397811yescharacteristic
840C2#2570811yescharacteristic
841C2#2571011yescharacteristic
842C2#2600111yescharacteristic
843C2#2600311yescharacteristic
844C2#2601711yescharacteristic
845C2#2601911yescharacteristic
846C2#2733411yescharacteristic
847C2#2733611yescharacteristic
848C2#2735511yescharacteristic
849C2#2735711yescharacteristic
850C2#3296111yescharacteristic
851C2#3296811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2059C2semidirect
3. C2×#1989C2semidirect
5. #11293C2semidirect
6. #11292C2semidirect
7. #11227C2semidirect
11. #10908C2semidirect
12. #10907C2semidirect
13. #10807C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#23462
C2×#20592
C2×#19892
#152162
#112932
#112922
#112272
#110962
#110952
#110422
#109082
#109072
#108072
#107312